The SEparator for CApture Reactions (SECAR) is a next-generation recoil separator system at the Facility for Rare Isotope Beams (FRIB) designed for the direct measurement of capture reactions on unstable nuclei in inverse kinematics. To maximize the performance of the device, careful beam alignment to the central ion optical axis needs to be achieved. This can be difficult to attain through manual tuning by human operators without potentially leaving the system in a sub-optimal and irreproducible state. In this work, we present the first development of online Bayesian optimization with a Gaussian process model to tune an ion beam through a nuclear astrophysics recoil separator. We show that the method achieves small incoming angular deviations (0-1 mrad) in an efficient and reproducible manner that is at least 3 times faster than standard hand-tuning. This method is now routinely used for all separator tuning.